ALE寬頻元素法於不可壓縮流之發展與應用

本文的主要目的在於發展ALE法的寬頻元素法用於處理具移動邊界的不可壓縮流問題，並應用此工具於流-固相互作用的研究。統御方程式的運動描述法採用ALE法是為了有效處理邊界的移動與減少網格的扭曲，而空間離散所採用的寬頻元素法具有高精確度的特性，在同一個數值精確度下需要計算的自由度比低階的方法相對來的少，程式上要處理的資料也就比較少，有助於提高流場的程式效率也有利於動態網格的應用，且使用的網格也可較大，可減輕網格的扭曲問題；本文以一維、二維的伯格方程式及二維不可壓縮之Navier-Stokes方程式驗證、討論程式的正確性與移動網格對數值收斂的影響；在實例的應用上，將會測試、討論三個例子，包括凹陷移動的...

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Main Authors:	蘇炯彰, Su, Jiong-Zhang
Other Authors:	顏瑞和, 臺灣大學：機械工程學研究所
Format:	Thesis
Language:	Chinese English
Published:	2006
Subjects:	移動邊界 ALE 寬頻元素法渦漩剝離振動圓柱共振 moving boundary spectral element method vortex shedding oscillating cylinder lock-in Arctic
Online Access:	http://ntur.lib.ntu.edu.tw/handle/246246/61138 http://ntur.lib.ntu.edu.tw/bitstream/246246/61138/1/ntu-95-R93522307-1.pdf

id	ftntaiwanuniv:oai:140.112.114.62:246246/61138
record_format	openpolar
institution	Open Polar
collection	National Taiwan University Institutional Repository (NTUR)
op_collection_id	ftntaiwanuniv
language	Chinese English
topic	移動邊界 ALE 寬頻元素法渦漩剝離振動圓柱共振 moving boundary spectral element method vortex shedding oscillating cylinder lock-in
spellingShingle	移動邊界 ALE 寬頻元素法渦漩剝離振動圓柱共振 moving boundary spectral element method vortex shedding oscillating cylinder lock-in 蘇炯彰 Su, Jiong-Zhang ALE寬頻元素法於不可壓縮流之發展與應用
topic_facet	移動邊界 ALE 寬頻元素法渦漩剝離振動圓柱共振 moving boundary spectral element method vortex shedding oscillating cylinder lock-in
description	本文的主要目的在於發展ALE法的寬頻元素法用於處理具移動邊界的不可壓縮流問題，並應用此工具於流-固相互作用的研究。統御方程式的運動描述法採用ALE法是為了有效處理邊界的移動與減少網格的扭曲，而空間離散所採用的寬頻元素法具有高精確度的特性，在同一個數值精確度下需要計算的自由度比低階的方法相對來的少，程式上要處理的資料也就比較少，有助於提高流場的程式效率也有利於動態網格的應用，且使用的網格也可較大，可減輕網格的扭曲問題；本文以一維、二維的伯格方程式及二維不可壓縮之Navier-Stokes方程式驗證、討論程式的正確性與移動網格對數值收斂的影響；在實例的應用上，將會測試、討論三個例子，包括凹陷移動的管內流、流體流經一橫向振動圓柱與流體流經兩並肩排列橫向振動圓柱，前兩個例子在趨勢與大小上都與文獻的模擬結果符合，確認本文所發展的工具於實際問題的可靠性，最後用於觀察兩並肩排列橫向振動圓柱的現象，除數值結果的討論外，並與實驗結果比較同異之處。 The main purpose of this thesis is to develop a spectral element method based on the ALE formulation for incompressible flow with moving boundary problems and present the application for fluid-structure interaction problem. Arbitrary Lagrangian Eulerian(ALE) formulation can offer robust treatment of the moving boundary and handle distortions of the computational mesh. Spectral element method, delivering high-order convergence characteristics, allow utilization of relatively fewer degrees of freedom than low-order methods for a desired accuracy. This is an advantage in reduction of data,efficiency of the algorithms and the application of dynamic mesh. Also, relatively larger elements than low-order methods enables spectral element ALE algorithms to reduce the problem of distortions. One dimensional and two dimensional Burger’s equation, incompressible two dimensional Navier-Stokes equation are applied to test the numerical accuracy and the effect of moving mesh on numerical convergence. The following two examples, flow in a channel with a moving indentation and flow past an transverse oscillating cylinder, show quantitative agreement with the numerical results and demonstrate the effectiveness of the method in some of these application. Detailed results are presented for last case, flow past an transverse oscillating cylinder, and preliminarily compared with the experimental results. 摘要 I ABSTRACT II 目錄 IV 表目錄 VI 圖目錄 VII 符號說明 XI 第一章緒論 1 第二章 ALE描述法與統御方程式 12 2.1 ALE運動描述法 12 2.2 統御方程式 15 2.2.1 伯格方程式 15 2.2.2 NAVIER-STOKES方程式 16 2.3 網格速度的計算 17 第三章數值方法 21 3.1 時間離散 21 3.2 網格速度的處理 26 第四章數值方法的驗證 31 4.1 一維伯格方程式(1D Burger Equation) 31 4.2 二維伯格方程式(2D Burger Equation) 34 4.2.1 網格扭曲與收斂關係測試 34 4.2.2 二維伯格方程式的移動網格測試 36 4.3 Kovasznay流場 37 4.4 暫態邊界流場 39 第五章實例應用 54 5.1 凹陷移動的管內流 54 5.2 流體流經一橫向振動的圓柱 56 5.2.1 靜止圓柱 56 5.2.2 振動圓柱 58 5.3 流體流經兩並肩排列橫向振動的圓柱 61 5.3.1 靜止圓柱 62 5.3.2 振動圓柱 63 第六章結論與建議 95 參考文獻 98
author2	顏瑞和臺灣大學：機械工程學研究所
format	Thesis
author	蘇炯彰 Su, Jiong-Zhang
author_facet	蘇炯彰 Su, Jiong-Zhang
author_sort	蘇炯彰
title	ALE寬頻元素法於不可壓縮流之發展與應用
title_short	ALE寬頻元素法於不可壓縮流之發展與應用
title_full	ALE寬頻元素法於不可壓縮流之發展與應用
title_fullStr	ALE寬頻元素法於不可壓縮流之發展與應用
title_full_unstemmed	ALE寬頻元素法於不可壓縮流之發展與應用
title_sort	ale寬頻元素法於不可壓縮流之發展與應用
publishDate	2006
url	http://ntur.lib.ntu.edu.tw/handle/246246/61138 http://ntur.lib.ntu.edu.tw/bitstream/246246/61138/1/ntu-95-R93522307-1.pdf
genre	Arctic
genre_facet	Arctic
op_relation	[1] W. F. Noh, "A time-dependent two-space dimensional coupled Eulerian-Lagrangian code," presented at Methods in Computational Physics, New York, 1964. [2] J. Trulio, "Theory and Structure of the AFTON Codes," Air Force Weapons Laboratory AFWL-TR-66-19, 1966. [3] C. W. Hirt, A. A. Amsden, and J. L. Cook, "Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds," Journal of Computational Physics, vol. 14, pp. 227-253, 1974. [4] J.Donea, P. Fasoli-Stella, and S. Giuliani, "Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems," presented at Trans. 4th Int. Conf. on Structural Mechanics in Reactor Technology, San Francisco, 1977. [5] T. Belytschko, J. M. Kennedy, and D. F. Schoeberle, "Quasi-Eulerian Finite-Element Formulation for Fluid-Structure Interaction," Mechanical Engineering, vol. 100, pp. 119-119, 1978. [6] T. J. R. Hughes, W. K. Liu, and T. K. Zimmermann, "Lagrangian-Eulerian Finite-Element Formulation for Incompressible Viscous Flows," Computer Methods in Applied Mechanics and Engineering, vol. 29, pp. 329-349, 1981. [7] W. K. Liu, T. Belytschko, and H. Chang, "An Arbitrary Lagrangian-Eulerian Finite-Element Method for Path-Dependent Materials," Computer Methods in Applied Mechanics and Engineering, vol. 58, pp. 227-245, 1986. [8] F. P. T. Baaijems, "An U-Ale Formulation of 3-D Unsteady Viscoelastic Flow," International Journal for Numerical Methods in Engineering, vol. 36, pp. 1115-1143, 1993. [9] E. Kuhl, H. Askes, and P. Steinmann, "An ALE formulation based on spatial and material settings of continuum mechanics. Part 1: Generic hyperelastic formulation," Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 4207-4222, 2004. [10] M. S. Gadala, "Recent trends in ALE formulation and its applications in solid mechanics," Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 4247-4275, 2004. [11] A. Abdulgalil and M. S. Gadala, "Modeling of dynamic fracture problems using ALE Finite Elements," Engineering Fracture Mechanics, submitted for publication. [12] J. Donea, S. Guiliani, and J. P. Halleux, "An Arbitrary Lagrangian-Eulerian Finite-Element Method for Transient Dynamic Fluid Structure Interactions," Computer Methods in Applied Mechanics and Engineering, vol. 33, pp. 689-723, 1982. [13] L.-W. Ho, "A Legendre Spectral Element Method for Simulation of Incompressible Unsteady Free-Surface Flows," in mechanical engineering: Massachusetts Institute of Technology, 1989. [14] Y. Zhao and A. Forhad, "A general method for simulation of fluid flows with moving and compliant boundaries on unstructured grids," Computer Methods in Applied Mechanics and Engineering, vol. 192, pp. 4439-4466, 2003. [15] C. H. Jung, T. Minowa, and T. Tanahashi, "Numerical analysis of molten metal under magnetic field using ALE method," Jsme International Journal Series a-Solid Mechanics and Material Engineering, vol. 45, pp. 153-160, 2002. [16] T. C. E.Warburton, "Spectral/hp Methods on Polymorphic Multi Domains: Algorithms and Applications," in Division of Applied Mathematics: Brown University, 1999. [17] G. E. Karniadakis, M. Israeli, and S. A. Orszag, "High-Order Splitting Methods for the Incompressible Navier Stokes Equations," Journal of Computational Physics, vol. 97, pp. 414-443, 1991. [18] A. G. Tomboulides, M. Israeli, and G. E. Karniadakis, "Efficient removal of boundary-divergence errors in time-splitting methods," Journal of Scientific Computing, vol. 4, pp. 291-308, 1989. [19] G. H. Koopmann, "Vortex Wakes of Vibrating Cylinders at Low Reynolds Numbers," Journal of Fluid Mechanics, vol. 28, pp. 501-&, 1967. [20] P. W. Bearman, M. J. Downie, J. M. R. Graham, and E. D. Obasaju, "Forces on Cylinders in Viscous Oscillatory Flow at Low Keulegan-Carpenter Numbers," Journal of Fluid Mechanics, vol. 154, pp. 337-356, 1985. [21] C. H. K. Williamson, "Defining a Universal and Continuous Strouhal-Reynolds Number Relationship for the Laminar Vortex Shedding of a Circular-Cylinder," Physics of Fluids, vol. 31, pp. 2742-2744, 1988. [22] C. H. K. Williamson and R. Govardhan, "Vortex-induced vibrations," Annual Review of Fluid Mechanics, vol. 36, pp. 413-455, 2004. [23] C. Evangelinos, D. Lucor, and G. E. Karniadakis, "DNS-derived force distribution on flexible cylinders subject to vortex-induced vibration," Journal of Fluids and Structures, vol. 14, pp. 429-+, 2000. [24] M. S. Bloor, "The Transition to Turbulence in the Wake of a Circular Cylinder," Journal of Fluid Mechanics, vol. 19, pp. 290-304, 1964. [25] X. Y. Lu and C. Dalton, "Calculation of the timing of vortex formation from an oscillating cylinder," Journal of Fluids and Structures, vol. 10, pp. 527-541, 1996. [26] W. Gu, C. Chyu, and D. Rockwell, "Timing of Vortex Formation from an Oscillating Cylinder," Physics of Fluids, vol. 6, pp. 3677-3682, 1994. [27] H. M. Blackburn and R. D. Henderson, "A study of two-dimensional flow past an oscillating cylinder," Journal of Fluid Mechanics, vol. 385, pp. 255-286, 1999. [28] Y. Liu, R. M. C. So, Y. L. Lau, and Y. Zhou, "Numerical studies of two side-by-side elastic cylinders in a cross-flow," Journal of Fluids and Structures, vol. 15, pp. 1009-1030, 2001. [29] N. Mahir and D. Rockwell, "Vortex formation from a forced system of two cylinders .2. Side-by-side arrangement," Journal of Fluids and Structures, vol. 10, pp. 491-500, 1996. [30] J. R. Meneghini and P. W. Bearman, "Numerical-Simulation of High Amplitude Oscillatory Flow About a Circular-Cylinder," Journal of Fluids and Structures, vol. 9, pp. 435-455, 1995. [31] E. Guilmineau and P. Queutey, "A numerical simulation of vortex shedding from an oscillating circular cylinder," Journal of Fluids and Structures, vol. 16, pp. 773-794, 2002. [32] R. King and D. J. Johns, "Wake Interaction Experiments with 2 Flexible Circular-Cylinders in Flowing Water," Journal of Sound and Vibration, vol. 45, pp. 259-283, 1976. [33] M. M. Zdravkovich, "Flow Induced Oscillations of 2 Interfering Circular-Cylinders," Journal of Sound and Vibration, vol. 101, pp. 511-521, 1985. [34] N. Mahir and D. Rockwell, "Vortex formation from a forced system of two cylinders .1. Tandem arrangement," Journal of Fluids and Structures, vol. 10, pp. 473-&, 1996. [35] W. Jester and Y. Kallinderis, "Numerical study of incompressible flow about transversely oscillating cylinder pairs," Journal of Offshore Mechanics and Arctic Engineering-Transactions of the Asme, vol. 126, pp. 310-317, 2004. [36] G. V. Papaioannou, D. K. P. Yue, M. S. Triantafyllou, and G. E. Karniadakis, "Evidence of holes in the Arnold tongues of flow past two oscillating cylinders," Physical Review Letters, vol. 96, 2006. [37] A. T. Patera, "A Spectral Element Method for Fluid-Dynamics - Laminar-Flow in a Channel Expansion," Journal of Computational Physics, vol. 54, pp. 468-488, 1984. [38] E. Rønquist, "Optimal spectral element methods for the unsteady three-dimensional incompressible Navier–Stokes equations," in Mechanical Engineering, vol. Ph.D. Cambridge, MA: Massachusetts Institute of Technology, 1988. [39] R. Lohner and C. Yang, "Improved ALE mesh velocities for moving bodies," Communications In Numerical Methods In Engineering, vol. 12, pp. 599-608, 1996. [40] P. M. Gresho and R. L. Sani, "On Pressure Boundary-Conditions for the Incompressible Navier-Stokes Equations," International Journal for Numerical Methods in Fluids, vol. 7, pp. 1111-1145, 1987. [41] T. J. Pedley and K. D. Stephanoff, "Flow Along a Channel with a Time-Dependent Indentation in One Wall - the Generation of Vorticity Waves," Journal of Fluid Mechanics, vol. 160, pp. 337-367, 1985. [42] I. Demirdzic and M. Peric, "Finite Volume Method for Prediction of Fluid-Flow in Arbitrarily Shaped Domains with Moving Boundaries," International Journal for Numerical Methods in Fluids, vol. 10, pp. 771-790, 1990. [43] M. Engel and M. Griebel, "Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems," International Journal for Numerical Methods in Fluids, vol. 50, pp. 437-468, 2006. [44] S. Kang, "Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers," Physics of Fluids, vol. 15, pp. 2486-2498, 2003. [45] 劉姿吟, "橫向流流經單一強制振動圓柱之流場結構模擬分析," 國立中央大學機械工程研究所,碩士論文, 2003.
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spelling	ftntaiwanuniv:oai:140.112.114.62:246246/61138 2023-05-15T14:28:29+02:00 ALE寬頻元素法於不可壓縮流之發展與應用 Development and Applications of ALE Spectral Element Method for Simulation of Incompressible 蘇炯彰 Su, Jiong-Zhang 顏瑞和臺灣大學：機械工程學研究所 2006 1582590 bytes application/pdf http://ntur.lib.ntu.edu.tw/handle/246246/61138 http://ntur.lib.ntu.edu.tw/bitstream/246246/61138/1/ntu-95-R93522307-1.pdf zh-TW en_US chi eng [1] W. F. Noh, "A time-dependent two-space dimensional coupled Eulerian-Lagrangian code," presented at Methods in Computational Physics, New York, 1964. [2] J. Trulio, "Theory and Structure of the AFTON Codes," Air Force Weapons Laboratory AFWL-TR-66-19, 1966. [3] C. W. Hirt, A. A. Amsden, and J. L. Cook, "Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds," Journal of Computational Physics, vol. 14, pp. 227-253, 1974. [4] J.Donea, P. Fasoli-Stella, and S. Giuliani, "Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems," presented at Trans. 4th Int. Conf. on Structural Mechanics in Reactor Technology, San Francisco, 1977. [5] T. Belytschko, J. M. Kennedy, and D. F. Schoeberle, "Quasi-Eulerian Finite-Element Formulation for Fluid-Structure Interaction," Mechanical Engineering, vol. 100, pp. 119-119, 1978. [6] T. J. R. Hughes, W. K. Liu, and T. K. Zimmermann, "Lagrangian-Eulerian Finite-Element Formulation for Incompressible Viscous Flows," Computer Methods in Applied Mechanics and Engineering, vol. 29, pp. 329-349, 1981. [7] W. K. Liu, T. Belytschko, and H. Chang, "An Arbitrary Lagrangian-Eulerian Finite-Element Method for Path-Dependent Materials," Computer Methods in Applied Mechanics and Engineering, vol. 58, pp. 227-245, 1986. [8] F. P. T. Baaijems, "An U-Ale Formulation of 3-D Unsteady Viscoelastic Flow," International Journal for Numerical Methods in Engineering, vol. 36, pp. 1115-1143, 1993. [9] E. Kuhl, H. Askes, and P. Steinmann, "An ALE formulation based on spatial and material settings of continuum mechanics. Part 1: Generic hyperelastic formulation," Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 4207-4222, 2004. [10] M. S. Gadala, "Recent trends in ALE formulation and its applications in solid mechanics," Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 4247-4275, 2004. [11] A. Abdulgalil and M. S. Gadala, "Modeling of dynamic fracture problems using ALE Finite Elements," Engineering Fracture Mechanics, submitted for publication. [12] J. Donea, S. Guiliani, and J. P. Halleux, "An Arbitrary Lagrangian-Eulerian Finite-Element Method for Transient Dynamic Fluid Structure Interactions," Computer Methods in Applied Mechanics and Engineering, vol. 33, pp. 689-723, 1982. [13] L.-W. Ho, "A Legendre Spectral Element Method for Simulation of Incompressible Unsteady Free-Surface Flows," in mechanical engineering: Massachusetts Institute of Technology, 1989. [14] Y. Zhao and A. Forhad, "A general method for simulation of fluid flows with moving and compliant boundaries on unstructured grids," Computer Methods in Applied Mechanics and Engineering, vol. 192, pp. 4439-4466, 2003. [15] C. H. Jung, T. Minowa, and T. Tanahashi, "Numerical analysis of molten metal under magnetic field using ALE method," Jsme International Journal Series a-Solid Mechanics and Material Engineering, vol. 45, pp. 153-160, 2002. [16] T. C. E.Warburton, "Spectral/hp Methods on Polymorphic Multi Domains: Algorithms and Applications," in Division of Applied Mathematics: Brown University, 1999. [17] G. E. Karniadakis, M. Israeli, and S. A. Orszag, "High-Order Splitting Methods for the Incompressible Navier Stokes Equations," Journal of Computational Physics, vol. 97, pp. 414-443, 1991. [18] A. G. Tomboulides, M. Israeli, and G. E. Karniadakis, "Efficient removal of boundary-divergence errors in time-splitting methods," Journal of Scientific Computing, vol. 4, pp. 291-308, 1989. [19] G. H. Koopmann, "Vortex Wakes of Vibrating Cylinders at Low Reynolds Numbers," Journal of Fluid Mechanics, vol. 28, pp. 501-&, 1967. [20] P. W. Bearman, M. J. Downie, J. M. R. Graham, and E. D. Obasaju, "Forces on Cylinders in Viscous Oscillatory Flow at Low Keulegan-Carpenter Numbers," Journal of Fluid Mechanics, vol. 154, pp. 337-356, 1985. [21] C. H. K. Williamson, "Defining a Universal and Continuous Strouhal-Reynolds Number Relationship for the Laminar Vortex Shedding of a Circular-Cylinder," Physics of Fluids, vol. 31, pp. 2742-2744, 1988. [22] C. H. K. Williamson and R. Govardhan, "Vortex-induced vibrations," Annual Review of Fluid Mechanics, vol. 36, pp. 413-455, 2004. [23] C. Evangelinos, D. Lucor, and G. E. Karniadakis, "DNS-derived force distribution on flexible cylinders subject to vortex-induced vibration," Journal of Fluids and Structures, vol. 14, pp. 429-+, 2000. [24] M. S. Bloor, "The Transition to Turbulence in the Wake of a Circular Cylinder," Journal of Fluid Mechanics, vol. 19, pp. 290-304, 1964. [25] X. Y. Lu and C. Dalton, "Calculation of the timing of vortex formation from an oscillating cylinder," Journal of Fluids and Structures, vol. 10, pp. 527-541, 1996. [26] W. Gu, C. Chyu, and D. Rockwell, "Timing of Vortex Formation from an Oscillating Cylinder," Physics of Fluids, vol. 6, pp. 3677-3682, 1994. [27] H. M. Blackburn and R. D. Henderson, "A study of two-dimensional flow past an oscillating cylinder," Journal of Fluid Mechanics, vol. 385, pp. 255-286, 1999. [28] Y. Liu, R. M. C. So, Y. L. Lau, and Y. Zhou, "Numerical studies of two side-by-side elastic cylinders in a cross-flow," Journal of Fluids and Structures, vol. 15, pp. 1009-1030, 2001. [29] N. Mahir and D. Rockwell, "Vortex formation from a forced system of two cylinders .2. Side-by-side arrangement," Journal of Fluids and Structures, vol. 10, pp. 491-500, 1996. [30] J. R. Meneghini and P. W. Bearman, "Numerical-Simulation of High Amplitude Oscillatory Flow About a Circular-Cylinder," Journal of Fluids and Structures, vol. 9, pp. 435-455, 1995. [31] E. Guilmineau and P. Queutey, "A numerical simulation of vortex shedding from an oscillating circular cylinder," Journal of Fluids and Structures, vol. 16, pp. 773-794, 2002. [32] R. King and D. J. Johns, "Wake Interaction Experiments with 2 Flexible Circular-Cylinders in Flowing Water," Journal of Sound and Vibration, vol. 45, pp. 259-283, 1976. [33] M. M. Zdravkovich, "Flow Induced Oscillations of 2 Interfering Circular-Cylinders," Journal of Sound and Vibration, vol. 101, pp. 511-521, 1985. [34] N. Mahir and D. Rockwell, "Vortex formation from a forced system of two cylinders .1. Tandem arrangement," Journal of Fluids and Structures, vol. 10, pp. 473-&, 1996. [35] W. Jester and Y. Kallinderis, "Numerical study of incompressible flow about transversely oscillating cylinder pairs," Journal of Offshore Mechanics and Arctic Engineering-Transactions of the Asme, vol. 126, pp. 310-317, 2004. [36] G. V. Papaioannou, D. K. P. Yue, M. S. Triantafyllou, and G. E. Karniadakis, "Evidence of holes in the Arnold tongues of flow past two oscillating cylinders," Physical Review Letters, vol. 96, 2006. [37] A. T. Patera, "A Spectral Element Method for Fluid-Dynamics - Laminar-Flow in a Channel Expansion," Journal of Computational Physics, vol. 54, pp. 468-488, 1984. [38] E. Rønquist, "Optimal spectral element methods for the unsteady three-dimensional incompressible Navier–Stokes equations," in Mechanical Engineering, vol. Ph.D. Cambridge, MA: Massachusetts Institute of Technology, 1988. [39] R. Lohner and C. Yang, "Improved ALE mesh velocities for moving bodies," Communications In Numerical Methods In Engineering, vol. 12, pp. 599-608, 1996. [40] P. M. Gresho and R. L. Sani, "On Pressure Boundary-Conditions for the Incompressible Navier-Stokes Equations," International Journal for Numerical Methods in Fluids, vol. 7, pp. 1111-1145, 1987. [41] T. J. Pedley and K. D. Stephanoff, "Flow Along a Channel with a Time-Dependent Indentation in One Wall - the Generation of Vorticity Waves," Journal of Fluid Mechanics, vol. 160, pp. 337-367, 1985. [42] I. Demirdzic and M. Peric, "Finite Volume Method for Prediction of Fluid-Flow in Arbitrarily Shaped Domains with Moving Boundaries," International Journal for Numerical Methods in Fluids, vol. 10, pp. 771-790, 1990. [43] M. Engel and M. Griebel, "Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems," International Journal for Numerical Methods in Fluids, vol. 50, pp. 437-468, 2006. [44] S. Kang, "Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers," Physics of Fluids, vol. 15, pp. 2486-2498, 2003. [45] 劉姿吟, "橫向流流經單一強制振動圓柱之流場結構模擬分析," 國立中央大學機械工程研究所,碩士論文, 2003. 移動邊界 ALE 寬頻元素法渦漩剝離振動圓柱共振 moving boundary spectral element method vortex shedding oscillating cylinder lock-in thesis 2006 ftntaiwanuniv 2016-02-20T00:15:49Z 本文的主要目的在於發展ALE法的寬頻元素法用於處理具移動邊界的不可壓縮流問題，並應用此工具於流-固相互作用的研究。統御方程式的運動描述法採用ALE法是為了有效處理邊界的移動與減少網格的扭曲，而空間離散所採用的寬頻元素法具有高精確度的特性，在同一個數值精確度下需要計算的自由度比低階的方法相對來的少，程式上要處理的資料也就比較少，有助於提高流場的程式效率也有利於動態網格的應用，且使用的網格也可較大，可減輕網格的扭曲問題；本文以一維、二維的伯格方程式及二維不可壓縮之Navier-Stokes方程式驗證、討論程式的正確性與移動網格對數值收斂的影響；在實例的應用上，將會測試、討論三個例子，包括凹陷移動的管內流、流體流經一橫向振動圓柱與流體流經兩並肩排列橫向振動圓柱，前兩個例子在趨勢與大小上都與文獻的模擬結果符合，確認本文所發展的工具於實際問題的可靠性，最後用於觀察兩並肩排列橫向振動圓柱的現象，除數值結果的討論外，並與實驗結果比較同異之處。 The main purpose of this thesis is to develop a spectral element method based on the ALE formulation for incompressible flow with moving boundary problems and present the application for fluid-structure interaction problem. Arbitrary Lagrangian Eulerian(ALE) formulation can offer robust treatment of the moving boundary and handle distortions of the computational mesh. Spectral element method, delivering high-order convergence characteristics, allow utilization of relatively fewer degrees of freedom than low-order methods for a desired accuracy. This is an advantage in reduction of data,efficiency of the algorithms and the application of dynamic mesh. Also, relatively larger elements than low-order methods enables spectral element ALE algorithms to reduce the problem of distortions. One dimensional and two dimensional Burger’s equation, incompressible two dimensional Navier-Stokes equation are applied to test the numerical accuracy and the effect of moving mesh on numerical convergence. The following two examples, flow in a channel with a moving indentation and flow past an transverse oscillating cylinder, show quantitative agreement with the numerical results and demonstrate the effectiveness of the method in some of these application. Detailed results are presented for last case, flow past an transverse oscillating cylinder, and preliminarily compared with the experimental results. 摘要 I ABSTRACT II 目錄 IV 表目錄 VI 圖目錄 VII 符號說明 XI 第一章緒論 1 第二章 ALE描述法與統御方程式 12 2.1 ALE運動描述法 12 2.2 統御方程式 15 2.2.1 伯格方程式 15 2.2.2 NAVIER-STOKES方程式 16 2.3 網格速度的計算 17 第三章數值方法 21 3.1 時間離散 21 3.2 網格速度的處理 26 第四章數值方法的驗證 31 4.1 一維伯格方程式(1D Burger Equation) 31 4.2 二維伯格方程式(2D Burger Equation) 34 4.2.1 網格扭曲與收斂關係測試 34 4.2.2 二維伯格方程式的移動網格測試 36 4.3 Kovasznay流場 37 4.4 暫態邊界流場 39 第五章實例應用 54 5.1 凹陷移動的管內流 54 5.2 流體流經一橫向振動的圓柱 56 5.2.1 靜止圓柱 56 5.2.2 振動圓柱 58 5.3 流體流經兩並肩排列橫向振動的圓柱 61 5.3.1 靜止圓柱 62 5.3.2 振動圓柱 63 第六章結論與建議 95 參考文獻 98 Thesis Arctic National Taiwan University Institutional Repository (NTUR)

ALE寬頻元素法於不可壓縮流之發展與應用

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